题目
Annual returns and summary statistics for three funds are listed in the following exhibit:「huixue_img/importSubject/1564548691237408768.png」The fund that shows the highest absolute dispersion is:
选项
A.Fund PQR if the measure of dispersion is the range.
B.Fund XYZ if the measure of dispersion is the variance.
C.Fund ABC if the measure of dispersion is the mean absolute deviation.
答案
C
解析
C is correct. The mean absolute deviation (MAD) of Fund ABC’s returns is greater than the MAD of both of the other funds.「huixue_img/importSubject/1564548691329683456.png」The numbers shown for variance are understood to be in “percent squared” terms so that when taking the square root, the result is standard deviation in percentage terms. Alternatively, by expressing standard deviation and variance in decimal form, one can avoid the issue of units; in decimal form, the variances for Fund ABC, Fund XYZ, and Fund PQR are 0.0317, 0.0243, and 0.0110, respectively.
C正确。 ABC基金回报的平均绝对偏差(MAD)大于其他两个基金的MAD。 ABC基金的MAD = [|-20-(-4)|＋|23-(-4)|＋|-14-(-4)|＋|5-(-4)|＋|-14-(-4)|]/5=14.4% XYZ基金的MAD =[|-33-(-10.8)|＋|-12-(-10.8)|＋|-12-(-10.8)|＋|-8-(-10.8)|＋|11-(-10.8)|]/5=9.8% PQR基金的MAD=[|-14-(-5)|＋|-18-(-5)|＋|6-(-5)|＋|-2-(-5)|＋|3-(-5)|]/5=8.8% A和B错误: 方差的数字被理解为“百分比的平方”的形式，所以当取平方根时，结果就是百分比的标准偏差。或者，用小数表示标准差和方差，就可以避免单位的问题;以小数形式表示，基金ABC、基金XYZ和基金PQR的方差分别为0.0317、0.0243和0.0110。